Inflation or GDP are indeed just two of the many examples where big data would make an important contribution. Advanced economies measure these indicators relatively accurately but there is huge potential in developing countries, including in much more granular analysis, e.g. the geographic distribution of food prices which varies extremely in many countries due to a combination of government and market failures.
However, there are many more NEW areas where traditional methods of analysis have difficulty making great advancement within a reasonable timeframe. This includes the measurement of teacher attendance, improving learning methods, responding faster to potholes or anticipating traffic flows. And then there is the huge area of healthcare where a lot of exploration is already underway but more needs to be done in developing countries.
These are examples where I am sure that big data will make a big difference. Feel free to send me your ideas.